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arXiv · 1509.07069

Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity

Marius Junge·Bogdan Udrea
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Abstract

We define $Γ_q(B,S \otimes H)$, the generalized $q$-gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(π_j,B,A,D)$ and to a subset $1 \in S = S^* \subset A$ and, under certain assumptions, prove their strong solidity relative to $B$. We provide many examples of strongly solid generalized $q$-gaussian von Neumann algebras. We also obtain non-isomorphism and non-embedability results about some of these von Neumann algebras.

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Marius Junge, Bogdan Udrea. 2018-09-19. Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity. https://arxiv.org/abs/1509.07069

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